Taking the Long Shot

It ocurred to me that if I talk about the same topic every time, I will severely limit the range of viewership. I read an article the other day about the new distance record for a kill shot. The Canadian Special Forces Command confirmed a shot from a member of it’s Joint Task Force connected to a verified distance of 3,540 meters during the summer, making it the longest successful sniper kill on record. That is 2.2 miles, more than 38 football fields, 139,392 inches, somewhere around 11 seconds of flight time, and if that’s accurate, the bullet was subsonic long enough that the sound caught back up allowing the terrorist to hear the rifle report for a few milliseconds before impact. Former U.S. Army Ranger and author of the “Long Range Shooting Handbook” Ryan Cleckner, said another person involved deserves a lot of credit. The spotter would have had to successfully calculate five factors: distance, wind, atmospheric conditions, and the speed of the earth’s rotation at their latitude,” he told Fox News. The latitude of Salt Lake City is 40.758701 give or take depending on exactly where you are. To make one complete rotation in 24 hours, a point near the equator of the Earth must move at close to 1000 miles per hour (1600 km/hr). The speed gets less as you move north, but it’s still a good clip throughout the United States. Because gravity holds us tight to the surface of our planet, we move with the Earth and don’t notice its rotation in everyday life.

When a person is standing at the equator, the earth spins at about 1,038 miles per hour (or 1,670 kph). The speed depends where one is located on the planet. The earth’s speed is at its fastest around the equator because that is where the circumference of the planet is greatest, which is 24,902 miles. It takes the earth one day to complete one full rotation. for those standing at the north pole, the speed of the earth’s rotation is almost zero. In the mid-latitudes of the United States and Europe, they spin at about 700 to 900 mph, or 1,125 to 1,450 kph.

Rotational Speed Versus Latitude

We know how long it takes the Earth to rotate around its axis; it takes 23.93 hours. The circumference of the Earth at the equator is 40,075 km (24,901 mi). So take 40,075/23.93 and the rotational speed is 1,675 km/hr or 1,040 mph. We also know that at different locations on Earth the circumference changes, so the rotational speed changes.

Here are the rotational speeds at different latitudes.

• At 80° – 289.9 km/hr (180.1 mph).

• At 70° – 571.1 km/hr (354.8 mph).

• At 60° – 834.9 km/hr (518.7 mph).

• At 50° – 1073.3 km/hr (666.9 mph).

• At 40° – 1279.1 km/hr (794.8 mph).

• At 30° – 1446.1 km/hr (898.5 mph).

• At 20° – 1569.1 km/hr (974.9 mph).

• At 10° – 1644.4 km/hr (1021.7 mph).

• At 0° – 1675 km/hr (1040 mph). (The Equator)

So, around Salt Lake City, or 40 degrees latitude, the earth spins at roughly 795 miles per hour. It spins from west to east. So if you are shooting west, your bullet will arrive a little quicker, and a little slower if shooting east, since if you are shooting west, your target is approaching at 795 mph.

The air density ratio column in Table 3.1-1, which is the ratio of standard air density at altitude to the standard air density at sea level, shows that the air density decreases rapidly as altitude increases. Air density is a direct

Table 3.1-1 Standard Metro Atmospheric Parameters versus Altitude

Altitude		Air Density Ratio		Temperature		Baro Pressure				Speed of Sound
(Feet)		(At Altitude /		(Deg F)		(mm Hg)		(in Hg)		Ratio (At Altitude /
		At Sea Level)								At Sea Level)
Sea Level		1.0000		59.0		750.0		29.53		1.0000
1000		0.9702		55.4		722.7		28.45		0.9873
2000		0.9414		51.9		696.3		27.41		0.9744
3000		0.9133		48.3		670.9		26.41		0.9614
4000		0.8862		44.7		646.4		25.45		0.9483
5000		0.8598		41.2		622.7		24.52		0.9350
6000		0.8342		37.6		599.8		23.62		0.9216
7000		0.8094		34.1		577.8		22.75		0.9080
8000		0.7853		30.5		556.6		21.91		0.8943
9000		0.7619		26.9		536.1		21.11		0.8805
10000		0.7392		23.4		516.3		20.33		0.8666
11000		0.7172		19.8		497.3		19.58		0.8525
12000		0.6959		16.2		478.9		18.85		0.8383
13000		0.6752		12.7		461.1		18.16		0.8239
14000		0.6551		9.1		444.0		17.48		0.8094
15000		0.6356		5.5		427.6		16.83		0.7948

multiplier in the equation for the drag force on a bullet, and because of this, the drag force also decreases rapidly as altitude increases. This decrease in air density with altitude has by far the largest effect on a bullet trajectory, compared to the actual atmospheric conditions and the speed of sound versus altitude.

If you are shooting north or south, the earth will have rotated to the left or right quite a distance in 11 seconds. But, I’m not going to spoil it for you. Let’s see if you can figure it out.